InClassEx05

Importing the libraries

pacman::p_load(sf, tmap, spdep, funModeling, tidyverse, corrplot, ggpubr, blorr, GWmodel, skimr, caret)

Data Import

Importing water point data

Osun_wp_sf <- read_rds("data/rds/Osun_wp_sf.rds")

Importing Boundary data

Osun <- read_rds("data/rds/Osun.rds")

Checking the imported water point data

Osun_wp_sf %>%
  freq(input = 'status')
Warning: The `<scale>` argument of `guides()` cannot be `FALSE`. Use "none" instead as
of ggplot2 3.3.4.
ℹ The deprecated feature was likely used in the funModeling package.
  Please report the issue at <https://github.com/pablo14/funModeling/issues>.

  status frequency percentage cumulative_perc
1   TRUE      2642       55.5            55.5
2  FALSE      2118       44.5           100.0
#Viewing INteractive map
tmap_mode('view')
tmap mode set to interactive viewing
tm_shape(Osun) +
  tm_polygons(alpha = 0.4) +
  tm_shape(Osun_wp_sf) +
  tm_dots(col = 'status',
          alpha =0.6) +
  tm_view(set.zoom.limits = c(9,12))
#new way to quickly look at the data in a more 'report' format
Osun_wp_sf %>%
  skim()
Warning: Couldn't find skimmers for class: sfc_POINT, sfc; No user-defined `sfl`
provided. Falling back to `character`.
Data summary
Name Piped data
Number of rows 4760
Number of columns 75
_______________________
Column type frequency:
character 47
logical 5
numeric 23
________________________
Group variables None

Variable type: character

skim_variable n_missing complete_rate min max empty n_unique whitespace
source 0 1.00 5 44 0 2 0
report_date 0 1.00 22 22 0 42 0
status_id 0 1.00 2 7 0 3 0
water_source_clean 0 1.00 8 22 0 3 0
water_source_category 0 1.00 4 6 0 2 0
water_tech_clean 24 0.99 9 23 0 3 0
water_tech_category 24 0.99 9 15 0 2 0
facility_type 0 1.00 8 8 0 1 0
clean_country_name 0 1.00 7 7 0 1 0
clean_adm1 0 1.00 3 5 0 5 0
clean_adm2 0 1.00 3 14 0 35 0
clean_adm3 4760 0.00 NA NA 0 0 0
clean_adm4 4760 0.00 NA NA 0 0 0
installer 4760 0.00 NA NA 0 0 0
management_clean 1573 0.67 5 37 0 7 0
status_clean 0 1.00 9 32 0 7 0
pay 0 1.00 2 39 0 7 0
fecal_coliform_presence 4760 0.00 NA NA 0 0 0
subjective_quality 0 1.00 18 20 0 4 0
activity_id 4757 0.00 36 36 0 3 0
scheme_id 4760 0.00 NA NA 0 0 0
wpdx_id 0 1.00 12 12 0 4760 0
notes 0 1.00 2 96 0 3502 0
orig_lnk 4757 0.00 84 84 0 1 0
photo_lnk 41 0.99 84 84 0 4719 0
country_id 0 1.00 2 2 0 1 0
data_lnk 0 1.00 79 96 0 2 0
water_point_history 0 1.00 142 834 0 4750 0
clean_country_id 0 1.00 3 3 0 1 0
country_name 0 1.00 7 7 0 1 0
water_source 0 1.00 8 30 0 4 0
water_tech 0 1.00 5 37 0 20 0
adm2 0 1.00 3 14 0 33 0
adm3 4760 0.00 NA NA 0 0 0
management 1573 0.67 5 47 0 7 0
adm1 0 1.00 4 5 0 4 0
New Georeferenced Column 0 1.00 16 35 0 4760 0
lat_lon_deg 0 1.00 13 32 0 4760 0
public_data_source 0 1.00 84 102 0 2 0
converted 0 1.00 53 53 0 1 0
created_timestamp 0 1.00 22 22 0 2 0
updated_timestamp 0 1.00 22 22 0 2 0
Geometry 0 1.00 33 37 0 4760 0
ADM2_EN 0 1.00 3 14 0 30 0
ADM2_PCODE 0 1.00 8 8 0 30 0
ADM1_EN 0 1.00 4 4 0 1 0
ADM1_PCODE 0 1.00 5 5 0 1 0

Variable type: logical

skim_variable n_missing complete_rate mean count
rehab_year 4760 0 NaN :
rehabilitator 4760 0 NaN :
is_urban 0 1 0.39 FAL: 2884, TRU: 1876
latest_record 0 1 1.00 TRU: 4760
status 0 1 0.56 TRU: 2642, FAL: 2118

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
row_id 0 1.00 68550.48 10216.94 49601.00 66874.75 68244.50 69562.25 471319.00 ▇▁▁▁▁
lat_deg 0 1.00 7.68 0.22 7.06 7.51 7.71 7.88 8.06 ▁▂▇▇▇
lon_deg 0 1.00 4.54 0.21 4.08 4.36 4.56 4.71 5.06 ▃▆▇▇▂
install_year 1144 0.76 2008.63 6.04 1917.00 2006.00 2010.00 2013.00 2015.00 ▁▁▁▁▇
fecal_coliform_value 4760 0.00 NaN NA NA NA NA NA NA
distance_to_primary_road 0 1.00 5021.53 5648.34 0.01 719.36 2972.78 7314.73 26909.86 ▇▂▁▁▁
distance_to_secondary_road 0 1.00 3750.47 3938.63 0.15 460.90 2554.25 5791.94 19559.48 ▇▃▁▁▁
distance_to_tertiary_road 0 1.00 1259.28 1680.04 0.02 121.25 521.77 1834.42 10966.27 ▇▂▁▁▁
distance_to_city 0 1.00 16663.99 10960.82 53.05 7930.75 15030.41 24255.75 47934.34 ▇▇▆▃▁
distance_to_town 0 1.00 16726.59 12452.65 30.00 6876.92 12204.53 27739.46 44020.64 ▇▅▃▃▂
rehab_priority 2654 0.44 489.33 1658.81 0.00 7.00 91.50 376.25 29697.00 ▇▁▁▁▁
water_point_population 4 1.00 513.58 1458.92 0.00 14.00 119.00 433.25 29697.00 ▇▁▁▁▁
local_population_1km 4 1.00 2727.16 4189.46 0.00 176.00 1032.00 3717.00 36118.00 ▇▁▁▁▁
crucialness_score 798 0.83 0.26 0.28 0.00 0.07 0.15 0.35 1.00 ▇▃▁▁▁
pressure_score 798 0.83 1.46 4.16 0.00 0.12 0.41 1.24 93.69 ▇▁▁▁▁
usage_capacity 0 1.00 560.74 338.46 300.00 300.00 300.00 1000.00 1000.00 ▇▁▁▁▅
days_since_report 0 1.00 2692.69 41.92 1483.00 2688.00 2693.00 2700.00 4645.00 ▁▇▁▁▁
staleness_score 0 1.00 42.80 0.58 23.13 42.70 42.79 42.86 62.66 ▁▁▇▁▁
location_id 0 1.00 235865.49 6657.60 23741.00 230638.75 236199.50 240061.25 267454.00 ▁▁▁▁▇
cluster_size 0 1.00 1.05 0.25 1.00 1.00 1.00 1.00 4.00 ▇▁▁▁▁
lat_deg_original 4760 0.00 NaN NA NA NA NA NA NA
lon_deg_original 4760 0.00 NaN NA NA NA NA NA NA
count 0 1.00 1.00 0.00 1.00 1.00 1.00 1.00 1.00 ▁▁▇▁▁

Select and filter the values that we require

Osun_wp_sf_clean <- Osun_wp_sf %>%
  filter_at(vars(status,
                 distance_to_primary_road,
                 distance_to_secondary_road,
                 distance_to_tertiary_road,
                 distance_to_city,
                 distance_to_town,
                 water_point_population,
                 local_population_1km,
                 usage_capacity,
                 is_urban,
                 water_source_clean),
            all_vars(!is.na(.))) %>%
  mutate(usage_capacity = as.factor(usage_capacity))

Correlation Analysis

Osun_wp <- Osun_wp_sf_clean %>%
  select(c(7, 35:39, 42:43,46:47, 57)) %>%
  st_set_geometry(NULL)
cluster_vars.cor = cor(
  Osun_wp[,2:7])
corrplot.mixed(cluster_vars.cor,
               lower = 'ellipse',
               upper = 'number',
               tl.pos = 'lt',
               diag = 'l',
               tl.col = 'black')

Normal Log Regression

model <- glm(status ~ distance_to_primary_road +
              distance_to_secondary_road +
              distance_to_tertiary_road +
              distance_to_city +
              distance_to_town +
              is_urban +
              usage_capacity +
              water_source_clean +
              water_point_population +
              local_population_1km,
            data = Osun_wp_sf_clean,
            family = binomial(link = 'logit'))

Instead of using typical R report, we use blr_regress() from the blorr package

blr_regress(model)
                             Model Overview                              
------------------------------------------------------------------------
Data Set    Resp Var    Obs.    Df. Model    Df. Residual    Convergence 
------------------------------------------------------------------------
  data       status     4756      4755           4744           TRUE     
------------------------------------------------------------------------

                    Response Summary                     
--------------------------------------------------------
Outcome        Frequency        Outcome        Frequency 
--------------------------------------------------------
   0             2114              1             2642    
--------------------------------------------------------

                                 Maximum Likelihood Estimates                                   
-----------------------------------------------------------------------------------------------
               Parameter                    DF    Estimate    Std. Error    z value     Pr(>|z|) 
-----------------------------------------------------------------------------------------------
              (Intercept)                   1      0.3887        0.1124      3.4588       5e-04 
        distance_to_primary_road            1      0.0000        0.0000     -0.7153      0.4744 
       distance_to_secondary_road           1      0.0000        0.0000     -0.5530      0.5802 
       distance_to_tertiary_road            1      1e-04         0.0000      4.6708      0.0000 
            distance_to_city                1      0.0000        0.0000     -4.7574      0.0000 
            distance_to_town                1      0.0000        0.0000     -4.9170      0.0000 
              is_urbanTRUE                  1     -0.2971        0.0819     -3.6294       3e-04 
           usage_capacity1000               1     -0.6230        0.0697     -8.9366      0.0000 
water_source_cleanProtected Shallow Well    1      0.5040        0.0857      5.8783      0.0000 
   water_source_cleanProtected Spring       1      1.2882        0.4388      2.9359      0.0033 
         water_point_population             1      -5e-04        0.0000    -11.3686      0.0000 
          local_population_1km              1      3e-04         0.0000     19.2953      0.0000 
-----------------------------------------------------------------------------------------------

 Association of Predicted Probabilities and Observed Responses  
---------------------------------------------------------------
% Concordant          0.7347          Somers' D        0.4693   
% Discordant          0.2653          Gamma            0.4693   
% Tied                0.0000          Tau-a            0.2318   
Pairs                5585188          c                0.7347   
---------------------------------------------------------------
blr_confusion_matrix(model, cutoff = 0.5)
Confusion Matrix and Statistics 

          Reference
Prediction FALSE TRUE
         0  1301  738
         1   813 1904

                Accuracy : 0.6739 
     No Information Rate : 0.4445 

                   Kappa : 0.3373 

McNemars's Test P-Value  : 0.0602 

             Sensitivity : 0.7207 
             Specificity : 0.6154 
          Pos Pred Value : 0.7008 
          Neg Pred Value : 0.6381 
              Prevalence : 0.5555 
          Detection Rate : 0.4003 
    Detection Prevalence : 0.5713 
       Balanced Accuracy : 0.6680 
               Precision : 0.7008 
                  Recall : 0.7207 

        'Positive' Class : 1

Spatial Log Regression

Converting to spatial point data frame

Osun_wp_sp <- Osun_wp_sf_clean %>%
  select(c(status,
           distance_to_primary_road,
           distance_to_secondary_road,
           distance_to_tertiary_road,
           distance_to_city,
           distance_to_town,
           water_point_population,
           local_population_1km,
           usage_capacity,
           is_urban,
           water_source_clean)) %>%
  as_Spatial()

Osun_wp_sp
class       : SpatialPointsDataFrame 
features    : 4756 
extent      : 182502.4, 290751, 340054.1, 450905.3  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=4 +lon_0=8.5 +k=0.99975 +x_0=670553.98 +y_0=0 +a=6378249.145 +rf=293.465 +towgs84=-92,-93,122,0,0,0,0 +units=m +no_defs 
variables   : 11
names       : status, distance_to_primary_road, distance_to_secondary_road, distance_to_tertiary_road, distance_to_city, distance_to_town, water_point_population, local_population_1km, usage_capacity, is_urban, water_source_clean 
min values  :      0,        0.014461356813335,          0.152195902540837,         0.017815121653488, 53.0461399623541, 30.0019777713073,                      0,                    0,           1000,        0,           Borehole 
max values  :      1,         26909.8616132094,           19559.4793799085,          10966.2705628969,  47934.343603562, 44020.6393368124,                  29697,                36118,            300,        1,   Protected Spring 
bw.fixed <- bw.ggwr(status ~
                      distance_to_primary_road +
                      distance_to_secondary_road +
                      distance_to_tertiary_road +
                      distance_to_city +
                      distance_to_town +
                      water_point_population +
                      local_population_1km +
                      is_urban +
                      usage_capacity +
                      water_source_clean,
                    data = Osun_wp_sp,
                    family = 'binomial',
                    approach = 'AIC',
                    kernel = 'gaussian',
                    adaptive = FALSE,
                    longlat = FALSE)
Take a cup of tea and have a break, it will take a few minutes.
          -----A kind suggestion from GWmodel development group
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Retrieve the Bandwidth value

bw.fixed
[1] 2599.672
gwlr.fixed <- ggwr.basic(status ~
                      distance_to_primary_road +
                      distance_to_secondary_road +
                      distance_to_tertiary_road +
                      distance_to_city +
                      distance_to_town +
                      water_point_population +
                      local_population_1km +
                      is_urban +
                      usage_capacity +
                      water_source_clean,
                    data = Osun_wp_sp,
                    family = 'binomial',
                    bw = 2599.672,
                    kernel = 'gaussian',
                    adaptive = FALSE,
                    longlat = FALSE)
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Setting up Confusion Matrix for Viewing

To assess the performance of the gwLR, firstly, we will convert the SDF object in as data frame by using the code chunk below

gwr.fixed <- as.data.frame(gwlr.fixed$SDF)

Next we will label yhat values greater of equal to 0.5 into 1 and else 0. the result of the logic comparison operation

gwr.fixed <- gwr.fixed %>%
  mutate(most = ifelse(
    gwr.fixed$yhat >= 0.5, T, F))
gwr.fixed$y <- as.factor(gwr.fixed$y)
gwr.fixed$most <- as.factor(gwr.fixed$most)
CM <- confusionMatrix(data = gwr.fixed$most, reference = gwr.fixed$y)
CM
Confusion Matrix and Statistics

          Reference
Prediction FALSE TRUE
     FALSE  1824  263
     TRUE    290 2379
                                          
               Accuracy : 0.8837          
                 95% CI : (0.8743, 0.8927)
    No Information Rate : 0.5555          
    P-Value [Acc > NIR] : <2e-16          
                                          
                  Kappa : 0.7642          
                                          
 Mcnemar's Test P-Value : 0.2689          
                                          
            Sensitivity : 0.8628          
            Specificity : 0.9005          
         Pos Pred Value : 0.8740          
         Neg Pred Value : 0.8913          
             Prevalence : 0.4445          
         Detection Rate : 0.3835          
   Detection Prevalence : 0.4388          
      Balanced Accuracy : 0.8816          
                                          
       'Positive' Class : FALSE           
                                          
Osun_wp_sf_selected <- Osun_wp_sf_clean %>%
  select(c(ADM2_EN, ADM2_PCODE,
             ADM1_EN, ADM1_PCODE,
             status))
gwr_sf.fixed <-cbind(Osun_wp_sf_selected, gwr.fixed)
tmap_mode('view')
tmap mode set to interactive viewing
prob_T <- tm_shape(Osun) +
  tm_polygons(alpha = 0.1) +
  tm_shape(gwr_sf.fixed) +
  tm_dots(col = 'yhat',
          border.col = 'gray60',
          border.lwd = 1) +
  tm_view(set.zoom.limits = c(8,14))
prob_T

Dropping the non-significant variables after checking the results from the 1st log regression

Osun_wp_sf_clean2 <- Osun_wp_sf_clean %>%
  select(c(-'distance_to_primary_road', -'distance_to_secondary_road'))
model2 <- glm(status ~ 
              distance_to_tertiary_road +
              distance_to_city +
              distance_to_town +
              is_urban +
              usage_capacity +
              water_source_clean +
              water_point_population +
              local_population_1km,
            data = Osun_wp_sf_clean2,
            family = binomial(link = 'logit'))

Visualise the output again

blr_regress(model2)
                             Model Overview                              
------------------------------------------------------------------------
Data Set    Resp Var    Obs.    Df. Model    Df. Residual    Convergence 
------------------------------------------------------------------------
  data       status     4756      4755           4746           TRUE     
------------------------------------------------------------------------

                    Response Summary                     
--------------------------------------------------------
Outcome        Frequency        Outcome        Frequency 
--------------------------------------------------------
   0             2114              1             2642    
--------------------------------------------------------

                                 Maximum Likelihood Estimates                                   
-----------------------------------------------------------------------------------------------
               Parameter                    DF    Estimate    Std. Error    z value     Pr(>|z|) 
-----------------------------------------------------------------------------------------------
              (Intercept)                   1      0.3540        0.1055      3.3541       8e-04 
       distance_to_tertiary_road            1      1e-04         0.0000      4.9096      0.0000 
            distance_to_city                1      0.0000        0.0000     -5.2022      0.0000 
            distance_to_town                1      0.0000        0.0000     -5.4660      0.0000 
              is_urbanTRUE                  1     -0.2667        0.0747     -3.5690       4e-04 
           usage_capacity1000               1     -0.6206        0.0697     -8.9081      0.0000 
water_source_cleanProtected Shallow Well    1      0.4947        0.0850      5.8228      0.0000 
   water_source_cleanProtected Spring       1      1.2790        0.4384      2.9174      0.0035 
         water_point_population             1      -5e-04        0.0000    -11.3902      0.0000 
          local_population_1km              1      3e-04         0.0000     19.4069      0.0000 
-----------------------------------------------------------------------------------------------

 Association of Predicted Probabilities and Observed Responses  
---------------------------------------------------------------
% Concordant          0.7349          Somers' D        0.4697   
% Discordant          0.2651          Gamma            0.4697   
% Tied                0.0000          Tau-a            0.2320   
Pairs                5585188          c                0.7349   
---------------------------------------------------------------

ok, the nin-significant values had been removed

Converting to spatial point data frame

Osun_wp_sp2 <- Osun_wp_sf_clean2 %>%
  select(c(status,
           distance_to_tertiary_road,
           distance_to_city,
           distance_to_town,
           water_point_population,
           local_population_1km,
           usage_capacity,
           is_urban,
           water_source_clean)) %>%
  as_Spatial()

Osun_wp_sp2
class       : SpatialPointsDataFrame 
features    : 4756 
extent      : 182502.4, 290751, 340054.1, 450905.3  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=4 +lon_0=8.5 +k=0.99975 +x_0=670553.98 +y_0=0 +a=6378249.145 +rf=293.465 +towgs84=-92,-93,122,0,0,0,0 +units=m +no_defs 
variables   : 9
names       : status, distance_to_tertiary_road, distance_to_city, distance_to_town, water_point_population, local_population_1km, usage_capacity, is_urban, water_source_clean 
min values  :      0,         0.017815121653488, 53.0461399623541, 30.0019777713073,                      0,                    0,           1000,        0,           Borehole 
max values  :      1,          10966.2705628969,  47934.343603562, 44020.6393368124,                  29697,                36118,            300,        1,   Protected Spring 
bw2.fixed <- bw.ggwr(status ~
                      distance_to_tertiary_road +
                      distance_to_city +
                      distance_to_town +
                      water_point_population +
                      local_population_1km +
                      is_urban +
                      usage_capacity +
                      water_source_clean,
                    data = Osun_wp_sp2,
                    family = 'binomial',
                    approach = 'AIC',
                    kernel = 'gaussian',
                    adaptive = FALSE,
                    longlat = FALSE)
Take a cup of tea and have a break, it will take a few minutes.
          -----A kind suggestion from GWmodel development group
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Fixed bandwidth: 95768.67 AICc value: 5681.18 
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Fixed bandwidth: 59200.13 AICc value: 5645.901 
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Fixed bandwidth: 36599.53 AICc value: 5585.354 
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Fixed bandwidth: 22631.59 AICc value: 5481.877 
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Fixed bandwidth: 13998.93 AICc value: 5333.718 
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Fixed bandwidth: 8663.649 AICc value: 5178.493 
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Fixed bandwidth: 5366.266 AICc value: 5022.016 
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Fixed bandwidth: 3328.371 AICc value: 4827.587 
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Fixed bandwidth: 2068.882 AICc value: 4772.046 
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Fixed bandwidth: 1290.476 AICc value: 5809.715 
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Fixed bandwidth: 2549.964 AICc value: 4764.056 
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Fixed bandwidth: 2847.289 AICc value: 4791.834 
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Fixed bandwidth: 2366.207 AICc value: 4755.524 
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Fixed bandwidth: 2252.639 AICc value: 4759.188 
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Fixed bandwidth: 2393.017 AICc value: 4755.57 
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Fixed bandwidth: 2377.018 AICc value: 4755.48 

Retrieve the Bandwidth value

bw2.fixed
[1] 2377.371
gwlr2.fixed <- ggwr.basic(status ~
                      distance_to_tertiary_road +
                      distance_to_city +
                      distance_to_town +
                      water_point_population +
                      local_population_1km +
                      is_urban +
                      usage_capacity +
                      water_source_clean,
                    data = Osun_wp_sp2,
                    family = 'binomial',
                    bw = 2377.371,
                    kernel = 'gaussian',
                    adaptive = FALSE,
                    longlat = FALSE)
 Iteration    Log-Likelihood
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Setting up Confusion Matrix for Viewing

To assess the performance of the gwLR, firstly, we will convert the SDF object in as data frame by using the code chunk below

gwr2.fixed <- as.data.frame(gwlr2.fixed$SDF)

Next we will label yhat values greater of equal to 0.5 into 1 and else 0. the result of the logic comparison operation

gwr2.fixed <- gwr2.fixed %>%
  mutate(most = ifelse(
    gwr2.fixed$yhat >= 0.5, T, F))
gwr2.fixed$y <- as.factor(gwr2.fixed$y)
gwr2.fixed$most <- as.factor(gwr2.fixed$most)
CM <- confusionMatrix(data = gwr2.fixed$most, reference = gwr2.fixed$y)
CM
Confusion Matrix and Statistics

          Reference
Prediction FALSE TRUE
     FALSE  1833  268
     TRUE    281 2374
                                          
               Accuracy : 0.8846          
                 95% CI : (0.8751, 0.8935)
    No Information Rate : 0.5555          
    P-Value [Acc > NIR] : <2e-16          
                                          
                  Kappa : 0.7661          
                                          
 Mcnemar's Test P-Value : 0.6085          
                                          
            Sensitivity : 0.8671          
            Specificity : 0.8986          
         Pos Pred Value : 0.8724          
         Neg Pred Value : 0.8942          
             Prevalence : 0.4445          
         Detection Rate : 0.3854          
   Detection Prevalence : 0.4418          
      Balanced Accuracy : 0.8828          
                                          
       'Positive' Class : FALSE           
                                          
Osun_wp_sf_selected2 <- Osun_wp_sf_clean2 %>%
  select(c(ADM2_EN, ADM2_PCODE,
             ADM1_EN, ADM1_PCODE,
             status))
gwr_sf2.fixed <-cbind(Osun_wp_sf_selected2, gwr.fixed)
tmap_mode('view')
tmap mode set to interactive viewing
prob_T2 <- tm_shape(Osun) +
  tm_polygons(alpha = 0.1) +
  tm_shape(gwr_sf2.fixed) +
  tm_dots(col = 'yhat',
          border.col = 'gray60',
          border.lwd = 1) +
  tm_view(set.zoom.limits = c(8,14))
prob_T2